Montana Gov. Steve Bullock, a Democrat, has already endorsed his lieutenant governor, John Walsh for the Senate seat and is widely expected to appoint Mr. Walsh to fill the vacancy if Mr. Baucus leaves Washington. In a race where Republican Rep. Steve Daines, has long been favored to win, analysts have speculated that incumbency—even just a few months’ worth—could give Mr. Walsh the leg-up he needs.

How often do Senate appointees get elected? To answer that question, Washington Wire took a look at Senate history.

The answer is about half the time. Since 1956, appointed senators have won re-election at a rate of about 43%, according to analysis by David Parker, a political analyst and professor at Montana State University. That’s about half the rate at which Senate incumbents get re-elected, which is 85%.

Since 2000, eight appointed senators have been re-elected, one has not, and six did not seek re-election, according to Senate data.

Here are a few examples of when it’s worked:

Republicans Roger Wicker of Mississippi, John Barrasso of Wyoming, and Lisa Murkowski of Alaska were appointed and later elected, Rothenberg Political Report deputy editor Nathan Gonzalez writes. So were Democrats Robert Menendez of New Jersey and Kirsten Gillibrand of New York. But, Mr. Gonzalez points out, “each matched the partisan lean of his or her state in federal races.”

That’s not quite the case in Montana, where Mr. Daines was leading Mr. Walsh by 17 points, according to a November Public Policy Polling survey.

In January 2009, Democrat Michael Bennet was appointed to the Senate from Colorado. He was elected by a slim margin almost two years later, defeating Republican Ken Buck 48%-46%. Mr. Bennet had never held elective office before, and Mr. Gonzalez said he might easily have been defeated by a stronger Republican nominee.

And here are a few when it hasn’t:

Democrat Jean Carnahan was appointed to fill the seat of her late husband, Sen. Mel Carnahan, in January 2001. She lost the election almost two years later, 49%-50% to Republican Jim Talent. She had never held elective office.

In June 1996, Republican Sheila Frahm was appointed from Kansas to fill former Sen. Robert Dole’s seat after he resigned. She lost the primary less than five months later to Sam Brownback, who subsequently won the general election. Ms. Frahm, like Mr. Walsh, had been lieutenant governor.

Like Ms. Frahm, Mr. Walsh would only fill the Senate seat for a few months, since Mr. Baucus’s isn’t expected to clear the Senate before late January. That gives Mr. Walsh a short window in which to build a record. Mr. Walsh also faces a primary challenger in John Bohlinger, who also served as Montana lieutenant governor and has a higher favorability rating and name recognition.

Ultimately, Mr. Walsh’s fate in the 2014 race will depend on how he performs as a senator. “The fight will be to define what kind of Democrat John Walsh is,” Mr. Gonzalez said in an interview.

About Washington Wire

Washington Wire is one of the oldest standing features in American journalism. Since the Wire launched on Sept. 20, 1940, the Journal has offered readers an informal look at the capital. Now online, the Wire provides a succession of glimpses at what’s happening behind hot stories and warnings of what to watch for in the days ahead. The Wire is led by Reid J. Epstein, with contributions from the rest of the bureau. Washington Wire now also includes Think Tank, our home for outside analysis from policy and political thinkers.